IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i13p2966-d1185894.html
   My bibliography  Save this article

Axiomatization of Blockchain Theory

Author

Listed:
  • Sergey Goncharov

    (Sobolev Institute of Mathematics, 630090 Novosibirsk, Russia
    These authors contributed equally to this work.)

  • Andrey Nechesov

    (Sobolev Institute of Mathematics, 630090 Novosibirsk, Russia
    These authors contributed equally to this work.)

Abstract

The increasing use of artificial intelligence algorithms, smart contracts, the internet of things, cryptocurrencies, and digital money highlights the need for secure and sustainable decentralized solutions. Currently, the blockchain technology serves as the backbone for most decentralized systems. However, the question of axiomatization of the blockchain theory in the first-order logic has been open until today, despite the efficient computational implementations of these systems. This did not allow one to formalize the blockchain structure, as well as to model and verify it using logical methods. This work introduces a finitely axiomatizable blockchain theory T that defines a class of blockchain structures K using the axioms of the first-order logic. The models of the theory T are well-known blockchain implementations with the proof of work consensus algorithm, including Bitcoin, Ethereum (PoW version), Ethereum Classic, and some others. By utilizing mathematical logic, we can study these models and derive new theorems of the theory T through automatic proofs. Also, the axiomatization of blockchain opens up new opportunities to develop blockchain-based systems that can help solve some of the open problems in the fields of artificial intelligence, robotics, cryptocurrencies, etc.

Suggested Citation

  • Sergey Goncharov & Andrey Nechesov, 2023. "Axiomatization of Blockchain Theory," Mathematics, MDPI, vol. 11(13), pages 1-16, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:13:p:2966-:d:1185894
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/13/2966/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/13/2966/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Maxim Bichuch & Zachary Feinstein, 2022. "Axioms for Automated Market Makers: A Mathematical Framework in FinTech and Decentralized Finance," Papers 2210.01227, arXiv.org, revised Feb 2025.
    2. Jacob D. Leshno & Philipp Strack, 2020. "Bitcoin: An Axiomatic Approach and an Impossibility Theorem," American Economic Review: Insights, American Economic Association, vol. 2(3), pages 269-286, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hanna Halaburda & Guillaume Haeringer & Joshua Gans & Neil Gandal, 2022. "The Microeconomics of Cryptocurrencies," Journal of Economic Literature, American Economic Association, vol. 60(3), pages 971-1013, September.
    2. Georg Menz & Moritz Vo{ss}, 2023. "Aggregation of financial markets," Papers 2309.04116, arXiv.org, revised Sep 2024.
    3. Nicola Dimitri, 2022. "The Economics of Consensus in Algorand," FinTech, MDPI, vol. 1(2), pages 1-16, May.
    4. Auer, Raphael & Monnet, Cyril & Shin, Hyun Song, 2025. "Distributed ledgers and the governance of money," Journal of Financial Economics, Elsevier, vol. 167(C).
    5. Can, Burak & Leth Hougaard, Jens & Pourpouneh, Mohsen, 2022. "On reward sharing in blockchain mining pools," Games and Economic Behavior, Elsevier, vol. 136(C), pages 274-298.
    6. Joshua S. Gans & Hanna Halaburda, 2023. ""Zero Cost'' Majority Attacks on Permissionless Blockchains," NBER Working Papers 31473, National Bureau of Economic Research, Inc.
    7. Hans Gersbach & Akaki Mamageishvili & Fikri Pitsuwan, 2023. "Crowdsearch," Papers 2311.08532, arXiv.org.
    8. Auer, Raphael & Tercero-Lucas, David, 2022. "Distrust or speculation? The socioeconomic drivers of U.S. cryptocurrency investments," Journal of Financial Stability, Elsevier, vol. 62(C).
    9. Osiebuni Collins OBU & Wilfred I. UKPERE, 2022. "The Implications of the Incursion of Cryptocurrency on the Effectiveness of Fiscal Policy," Review of Applied Socio-Economic Research, Pro Global Science Association, vol. 23(1), pages 134-150, June.
    10. Kensuke Ito, 2024. "Cryptoeconomics and Tokenomics as Economics: A Survey with Opinions," Papers 2407.15715, arXiv.org.
    11. Joshua S. Gans & Richard Holden, 2022. "Mechanism Design Approaches to Blockchain Consensus," Papers 2206.10065, arXiv.org.
    12. Nicola Borri, 2025. "Corporate Finance in the Age of Fintech: Scenarios and Challenges," Papers 2503.18675, arXiv.org.
    13. Roger Lee, 2023. "All AMMs are CFMMs. All DeFi markets have invariants. A DeFi market is arbitrage-free if and only if it has an increasing invariant," Papers 2310.09782, arXiv.org, revised Dec 2023.
    14. Benigno, Pierpaolo & Schilling, Linda M. & Uhlig, Harald, 2022. "Cryptocurrencies, currency competition, and the impossible trinity," Journal of International Economics, Elsevier, vol. 136(C).
    15. Stinner, Jona & Tyrell, Marcel, 2022. "Proof-Of-Work Consensus Under Exogenous Distress: Evidence from Mining Shocks in the Bitcoin Ecosystem," VfS Annual Conference 2022 (Basel): Big Data in Economics 264115, Verein für Socialpolitik / German Economic Association.
    16. Schilling, Linda & Fernández-Villaverde, Jesús & Uhlig, Harald, 2024. "Central bank digital currency: When price and bank stability collide," Journal of Monetary Economics, Elsevier, vol. 145(C).
    17. Masaaki Fukasawa & Basile Maire & Marcus Wunsch, 2025. "Liquidity provision of utility indifference type in decentralized exchanges," Papers 2502.01931, arXiv.org.
    18. Peplluis R. Esteva & Alberto Ballesteros Rodr'iguez, 2023. "Invoice discounting using kelly criterion by automated market makers-like implementations," Papers 2302.09009, arXiv.org.
    19. Feng, Wenjun & Zhang, Zhengjun, 2023. "Currency exchange rate predictability: The new power of Bitcoin prices," Journal of International Money and Finance, Elsevier, vol. 132(C).
    20. Jason Milionis & Ciamac C. Moallemi & Tim Roughgarden, 2023. "Complexity-Approximation Trade-offs in Exchange Mechanisms: AMMs vs. LOBs," Papers 2302.11652, arXiv.org, revised Apr 2023.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:13:p:2966-:d:1185894. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.